1. Field of the Invention
The present invention relates to a control apparatus and a control method of a control system having a dead time.
2. Description of the Related Art
A control method that performs feedback control of the amount of twist of an arm of a robot by using a sliding mode control method has been proposed (in, for example, Japanese Patent Application Laid-Open No. HEI 3-180903). In this control method, a switching surface is calculated by using a value obtained through filter processing, including integration, of the amount of twist as in equation (1). In accordance with the switching surface, the control input value is changed or switched. Using the switched control input value, the control is carried out. The control based on the above-described method is applicable to the sliding mode control of a control object having a resonance frequency, as in the control of a robot arm. But if dynamics are ignored, the loop gain must be set smaller than the resonance frequency, and therefore the responsiveness cannot be enhanced. EQU J.times.d.sup.2.theta./dt.sup.2 =T (1)
where J is the inertia of the robot, .theta. is the rotation angle, and T is the input torque.
A control apparatus in which the sliding mode control method is employed by modifying a non-linear term so as to stabilize the non-linear term, such as changes of a friction coefficient or the like is also known (in, for example, from Japanese Patent Application Laid-Open No. HEI 10-301602). In this control apparatus, when an uncertainty occurs in a C matrix that relates an output and the quantity of a state of a control object to each other, the non-linear input gain used in the control system is raised higherlarge than a predetermined value used when there is no uncertainty in the C matrix until the Lyapunov's stability condition is met.
In the application of the sliding mode control method to a control system such as a clutch hydraulic control system or the like, having a non-linearity due to different operation conditions, the presence of a large dead time, or the like, there is a problem of a considerable decrease in the robustness of the control system. FIGS. 17 to 20 indicate results of a simulation of a case where the sliding mode control method is applied to a clutch slip speed control system and the slip speed x1 is controlled to a target value of 20 rpm. FIG. 17 is a graph indicating changes of the slip speed x1 over time. FIG. 18 is a graph indicating time-dependent changes of the time differential x2 of the slip speed x1. FIG. 19 is a graph indicating time-dependent changes of the control input value u. FIG. 20 is a graph indicating time-dependent changes of the switching surface .sigma.. As indicated in FIG. 17, the slip speed x1 does not immediately converge on the desired value, but converges only after repeated oscillations.
As a solution to this problem, it may be conceivable to apply the technique of the robot arm control model described above. However, this technique is intended for a linear control system having substantially no dead time. In this technique, therefore, there is no need to take into consideration changes of operation conditions (in a clutch hydraulic control system, for example, there are changes of the oil temperature, changes of the vehicle speed, changes of the slip speed range, changes of the engine load, changes due to aging, and the like), a large amount of dead time, and the like. Since the technique merely subjects observed values to an integrating processing, a similar theoretical development does not apply.
A control method designed so that the non-linear input becomes greater than a predetermined value used when there is no uncertainty in the C matrix, until the Lyapunov's stability condition is met, has a problem of requiring a complicated circuit.
As another related technology, a control apparatus that performs the sliding mode control of an air-fuel ratio control system of an internal combustion engine by using an estimated quantity of state supplied from an observer has been proposed (in, for example, "An Observer-Based Controller Design Method for Automotive Fuel-Injection System", Proceeding of the American Control Conference San Francisco, Calif., June 1993, which is hereby incorporated by reference) (the term "observer" as used hereafter refers to a device corresponding to that of this document). Since this control apparatus performs the sliding mode control by using an estimated quantity of state supplied from an observer, the control apparatus is able to solve a problem caused by performing the sliding mode control without using an observer, that is, prevent the chattering that occurs based on a fact that the amount of dead time is unignorably large relative to the responsiveness requirement of the engine air-fuel ratio control system. It is to be noted that the observer provides the estimated quantity of state by multiplying a value regarding the deviation between an estimated quantity of state and an actual quantity of state by a suitable gain, and feeding back the multiplication product.
If a sliding mode control method is applied to the presence of a large amount of dead time as in a shift control system of an automotive transmission or the like, there occurs a problem of a considerable decrease in the robustness of the system. FIGS. 21A and 21B indicate time-dependent changes of the rotation speed changing rate and time-dependent changes of the rotation speed, respectively, as results of a simulation where an ordinary sliding mode control method is applied. As can be seen from FIGS. 21A and 21B, mere application of an ordinary sliding mode control method does not achieve the proper following of the actual value of quantity of state with respect to the target value.
As a solution to this problem, it may be conceivable to use an observer as in the case of an engine air-fuel ratio control system described above. In this technique, however, the observer is constructed by simple addition of a linear term and a non-linear term. Therefore, the technique does not apply to a control object that is not compliant with a construction based on the addition. Furthermore, in this technique, only the dead time that is determined by a single factor, such as a dead time based on a time delay of an air-fuel ratio sensor, or the like, is taken into consideration, but the dead time determined in a complicated manner by a plurality of factors is not taken into consideration. Therefore, this technique is unable to estimate a precise quantity of state and, therefore, is unable to perform proper control.
FIGS. 22A and 22B indicate time-dependent changes of the rotation speed changing rate and time-dependent changes of the rotation speed as a result of a simulation where a sliding mode control method is applied, with a target value being used as an estimated quantity of state. FIGS. 23A and 23B indicate time-dependent changes of the rotation speed changing rate and time-dependent changes of the rotation speed as results of a simulation where a sliding mode control method is applied, with an actual value of quantity of state being used as an estimated quantity of state. As indicated in FIGS. 22A, 22B, 23A and 23B, even if a sliding mode control method is applied with a target value or an actual value of quantity of state being used as an estimated quantity of state, the actual value of the rotation speed changing rate drops considerably relative to the target value at around 1.25 seconds, causing a perceivable shock. Thus, proper control cannot be accomplished.